Elastic inconsistency of the force constant models for body centred tetragonal indium

The origin of the elastic inconsistency of a lattice dynamical model is analysed by resolving the atomic displacements of body centred tetragonal indium, along three mutually perpendicular directions. It is shown that the angular forces which include the three-body interactions as well as the mixed neighbour interactions, are mainly responsible for the elastic consistency of the CGW model, whereas the remaining models which neglect these interactions become elastically inconsistent as we go from cubic to tetragonal symmetry. Hence the former is unique and not equivalent to any of the latter, but a certain degree of equivalence exists among the force constants of the DAF, MAS, GTF and CGW models. The role played by two-body, three-body interactions and same neighbour, mixed neighbour interactions, the distortions introduced into the phonon dispersion curves of indium by the elastic inconsistency as well as the consequences of imposing the rotational invariance conditions on the force constants of a lattice dynamical model for non-cubic solids are discussed.